Ch.10 - Gases

Problem 51b

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Chapter 10, Problem 51b

(b) Calculate the molar mass of a gas if 2.50 g occupies 0.875 L at 685 torr and 35 °C

Verified step by step guidance

Step 1: Convert the temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is K = °C + 273.15.

Step 2: Convert the pressure from torr to atm. The conversion factor is 1 atm = 760 torr.

Step 3: Use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/K·mol), and T is the temperature in Kelvin. However, we need to rearrange the equation to solve for n (number of moles), which gives us n = PV/RT.

Step 4: Calculate the number of moles using the values from steps 1 and 2 and the rearranged ideal gas law equation from step 3.

Step 5: Calculate the molar mass of the gas. The molar mass is the mass of the gas divided by the number of moles. Use the mass given in the problem and the number of moles calculated in step 4.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate the properties of gases under various conditions, making it essential for solving problems involving gas behavior.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in a molecule. In the context of gases, knowing the molar mass is crucial for converting between mass and moles, which is necessary for applying the Ideal Gas Law to find the properties of the gas in question.

Gas Laws and Conditions

Gas laws describe the behavior of gases under various conditions of temperature and pressure. In this problem, the conditions include a specific volume (0.875 L), pressure (685 torr), and temperature (35 °C). Understanding how these conditions affect gas behavior is vital for accurately calculating the molar mass and applying the Ideal Gas Law effectively.

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Related Practice

Rank the following gases from least dense to most dense at 1.00 atm and 298 K: SO2,HBr,CO2.

Textbook Question

Which of the following statements best explains why a closed balloon filled with helium gas rises in air? (a) Helium is a monatomic gas, whereas nearly all the molecules that make up air, such as nitrogen and oxygen, are diatomic. (b) The average speed of helium atoms is greater than the average speed of air molecules, and the greater speed of collisions with the balloon walls propels the balloon upward. (c) Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume. (d) Because helium has a lower molar mass than the average air molecule, the helium atoms are in faster motion. This means that the temperature of the helium is greater than the air temperature. Hot gases tend to rise.

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Textbook Question

(a) Calculate the density of NO₂gas at 0.970 atm and 35 °C.

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Textbook Question

Calculate the molar mass of a vapor that has a density of 7.135 g/L at 12°C and 743 torr.

Textbook Question

In the Dumas-bulb technique for determining the molar mass of an unknown liquid, you vaporize the sample of a liquid that boils below 100°C in a boiling-water bath and determine the mass of vapor required to fill the bulb. From the following data, calculate the molar mass of the unknown liquid: mass of unknown vapor, 1.012 g; volume of bulb, 354 cm3; pressure, 742 torr; temperature, 99°C.

Textbook Question

The molar mass of a volatile substance was determined by the Dumas-bulb method described in Exercise 10.53. The unknown vapor had a mass of 0.846 g; the volume of the bulb was 354 cm3, pressure 752 torr, and temperature 100°C. Calculate the molar mass of the unknown vapor.